fekete-szeg¨o inequality for certain subclasses of analytic functions related with crescent-shaped domain and application of poison distribution series

The purpose of this paper is to define a new class of analytic, normalized functions in the open unit disk d = {z : z ∈ c and |z| < 1} subordinating with crescent shaped regions, and to derive certain coefficient estimates a2 , a3 and fekete-szeg¨o inequality for f ∈ mq(α, β, λ). a similar result have been done for the function f −1 . further application of our results to certain functions defined by convolution products with a normalized analytic function is given, in particular we obtain feketeszeg¨o inequalities for certain subclasses of functions defined through poisson distribution series.